A physics student is sitting on a rotating platform angular velocity question

1. The problem statement, all variables and given/known data
A physics student is sitting on a rotating platform. He is holding a heavy weight in each of his outstretched hands. At request of his physics instructor(!) he carries out various manoeuvres to try to change his angular velocity. Which of the following scenarios are described correctly?
Select True or False.

2. Relevant equations
E=1/2(mr^2)w^2

3. The attempt at a solution
1. he transfers both the weights to one outstretched hand. He then stretches his other hand back out to its original position. His angular velocity (after the manouvre is complete) has decreased.
FALSE

2. he transfers both the weights to one outstretched hand. He then stretches his other hand back out to its original position. His angular velocity (after the manouvre is complete) has not changed.
TRUE

3. he drops the weights. His angular velocity increases.
TRUE .

4. he drops the weights. His angular velocity reverses
FALSE

5. A friend throws a third weight so that the student catches it in one of his outstretched hands. No matter what the direction of the throw, the student's angular velocity increases.
FALSE

6. he drops the weights. His angular velocity decreases.
False

7. A friend throws a third weight so that the student catches it in one of his outstretched hands. No matter what the direction of the throw, the student's angular velocity decreases.
TRUE

8. he drops the weights. His angular velocity does not change.
FALSE

9. he raises his feet, and points them outwards from the chair as far as he can. His angular velocity reverses.
False

10. he brings the weights in to his chest. His angular velocity increases.
TRUE

Relevant equation should be angular momentum is conserved. The student can use internal energy to move the weights inwards or outwards, exchanging internal energy for angular kinetic energy. If a weight is thrown by another student, and the student on the spinning platform catches the weight, then a torque impulse occurs, and angular momentum is not conserved since there's an externally sourced torque involved.

If the weight lands on the platform it will still be rotating and the angular momentum of the platform/student system won't change. Do we know if the students arms extend out over the edge of the platform?

On second thoughts it's irrelevant. Whether or not the angular momentum leaves the system won't affect the rotational velocity.